Hummm is simply to understand your Auth is running. GS too.
GS crashing but don't send the message to the auth for disconnect it.
When you restart GS the Auth say: "Is strange i have already this GS logged on me"("duplicated index entry" i don't remember the exactly message but it's look like that)
After when a player try to connect the gs lunch 1 Message but the Auth believe have 2 GS with the same index. And he simply say the current account is already logged because he have 2 connections for 1 account.
I don't know if you are understand i hope it's help you